Introduction

As a result of the continuum assumption, field quantities such as density and velocity which reflect the mechanical or kinematic properties of continuum bodies are expressed mathematically as continuous functions, or at worst as piecewise continuous functions, of the space and time variables.

Moreover, the derivatives of such functions, if they enter into the theory at all, will be likewise continuous.

 

Inasmuch as this is an introductory textbook, we shall make two further assumptions on the materials we discuss in addition to the principal one of continuity. First, we require the materials to be homogeneous, that is to have identical properties at all locations. And secondly, that the materials be isotropic with respect to certain mechanical properties, meaning that those properties are the same in all directions at a given point. Later, we will relax this isotropy restriction to discuss briefly anisotropic materials which haveimportant meaning in the study of composite materials.